Streak sidebet

I'm curious whether anyone has determined hi-lo decision numbers for the Streak sidebet. I've seen such numbers in other posts, but they're based on at least slightly incorrect rules. Here are the current payoffs for the Streak sidebet:

win 2 hands in a row: paid 3 to 1
win 3 hands in a row: paid 8 to 1
win 4 hands in a row: paid 18 to 1
win 5 hands in a row: paid 38 to 1

Each of the four bets above is a separate bet. For example, if you choose the "4 in a row" bet and only win three in a row, then lose the fourth hand, you lose the bet. You'd only be paid for three wins in a row if you made the "3 in a row" bet (and the "2 in a row" bet, though you'd be paid for this prior to the third hand).

Pushes do not contribute to the length of a streak, but they do allow you to keep your streak alive.
On split hands, you must win the majority of the hands to count as a win. If you win as many split hands as you lose, it's counted as a push. If you lose more split hands than you win, it's a loss.
Insurance wins and losses are irrelevant to this side bet.
Double-down wins and losses are treated as single wins and losses for this sidebet.

General rules in play:
6 decks, S17, DAS, late surrender, resplit up to 4 hands, no resplit aces, shuffle at 1 to 1.25 decks.

Without counting, every Streak sidebet has a negative expected value, based on a 47.49 chance of winning a single hand (not counting pushes).

So my question is, "For what counts is each Streak sidebet profitable?"

Thanks in advance for your help.

I was also wondering what deviations from basic strategy would be profitable here.

For example, if you've bet "5 in a row" and have won four hands, it would make sense NOT to double-down on anything on the fifth hand. Risking losing the 38 to 1 payoff in exchange for getting a single extra bet would be a bad trade-off.

First, forget about the lower-end payoffs. You'd need to raise your win % to over 50% to beat the 2-hand wager, which is impossible as a practical matter.

I ran some sims on the 5-streak bet a while back. With the payoff schedule you describe the required win % is 48.1 for the 5-streak bet. Increase in win rate is roughly .25% for hi-lo. So, you need a TC of +3 to make a streak bet using no strategy alteration.
To test out the potential profitability of the bet I ran some sims a while ago which involved no doubling at all, which raises the win % to 47.8. This would have a huge negative effect on your main blackjack hand and was conducted for illustrative purposes only. Here, anything above TC + 1 is positive EV.

In both cases this is a waste of time. The problem is not that you can't get an edge - you definitely can. It is the variance. Correct Kelly betting requires you to bet your advantage divided by the ratio of a winning wager to a losing wager, in this case 38. You aren't ever likely to see an edge much in excess of 10%, so you have to bet very conservatively indeed to maintain a low risk of ruin because of the high possibility of a loss on each trial. And, the average trial isn't a single hand but some multiple of several hands, cutting down your hourly profit further. Finally, there is the complication of the drag factor in terms of variance on the main part of the blackjack wager.

Now, a more sophisticated play-by-play analysis could do better in terms of balance between maintaining EV and your streak bet, but I very doubt that it would be much better. Similarly, you could design a count specifically for the purposes of raising your win %, rather than maximizing your EV on a regular blackjack. But, from what I remember, the commercial count systems already do a pretty good job of maximizing win %.

Additionally, a 6-deck LS game with a one-deck cutoff is pretty darn good these days, even considering how the streak bet will slow things down. I'd just focus on the main part of the game.

I appreciate all of the analysis, especially with regard to variance, an aspect I hadn't considered.

Though the rules and penetration are good here, I should point out that this is in Colorado casinos, where the maximum bet is $5. However, they have gotten around this (partially) with Triple-Action Blackjack. You can also play up to three spots during slow periods, permitting a bet range from $5 to $45.

No fortune, true, but there are absolutely no anti-counting measures. You can vary your bets at will. The Streak bet was added in a further attempt to get more money on the table at once.

By the way, could you explain what you meant by "drag factor?"

P.S. Contrary to what you said, the "2 in a row" Streak bet is an absolute GOLD MINE for players. All you need is a count per deck of +14 or greater with six decks, which might happen as often as once every 10,000 hours of playing :-)

The ingenuity of AP's never ceases amaze me. I was forgetting about you poor chaps down in Colorado with that sucky $5 limit (I thought they were going to get rid of it?).

No fortune, true, but there are absolutely no anti-counting measures. You can vary your bets at will. The Streak bet was added in a further attempt to get more money on the table at once.

Given the general impossibility of trying to make money in Colorado, this is the best approach I can think of.
If you have a small, replenishable, bankroll, and are emotionally prepared for a loss, then you could do worse trying to build it up by attacking the streak sidebet. This would be better than travelling to a better game and having your bankroll eaten alive by expenses-and internet gambling isn't an option now if it ever was for you. You might get lucky and win enough to make travel expenses manageable. If not, try again, at some point you must grind ahead.

This approach is a very tough one. Your chances of tapping out are fair to excellent depending on exactly how aggressive your win goals are.

If you have a large bankroll then I would just try and find better games.

By the way, could you explain what you meant by "drag factor?"

The streak and blackjack bets are correlated with each other. If you win your 5 streak bet, you have also won 5 regular blackjack hands in a row. Conversely, if you aren't hitting your streak bets, you are likely to be doing badly at the regular game. This has an "eggs in one basket" effect which means you are taking on more risk than if you were betting on two truly independent things. Again, this leads a reduction in optimal bet size, and profitability.

You're right--the $5 limit does suck, but it's partially offset by the fact that you can make up to nine wagers per round (three triple-action spots, each with three bets). Combined with the otherwise decent rules of 6D/LS/DAS/80% penetration, the $5 to $45 bet spread is enough to yield at least marginal returns in the neighborhood of $10/hr.

The covariance of the Streak bets and regular bets is not ideal either, but still offers another advantage bet at modestly high counts.

I did some analysis, and the 4 in a row bet seems to be the best.

For 4 in a row at 18:1, you need a win rate of (1/19)^(1/4) = .479 to be profitable.

For 3 in a row at 8:1, you need a win rate of (1/9)^(1/3) = .481.

For 5 in a row at 38:1, you need a win rate of (1/39)^(1/5) = .481 (as you correctly stated).

Derived from the stats at http://www.bjstats.com/bjsc.asp, here are the high-low decision numbers for the Streak bet:

3 in a row: +6 or greater
4 in a row: +5 or greater
5 in a row: +6 or greater

And, if you're willing to devote a year or two to waiting for the 2 in a row bet: +14 or greater.

If you have any other comments or questions, you can email me at david@gorillablackjack.com